Question

$\huge{\underline{\underline{\bf Question}}}$

if $\sf x = acos³\theta$ and $\sf y = bsin³\theta$ then show that :-
$\sf \bigg( \dfrac{x}{a} \bigg)^{ \dfrac{2}{3} } + \bigg( \dfrac{y}{b} \bigg)^{ \dfrac{2}{3} } = 1$
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Answer 1

⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Given \:That★}}}}}$

$\sf x = acos³\theta$ and $\sf y = bsin³\theta$

${\rm{\red{\underline{\underline{To\:Prove : }}}}}$

$\sf \bigg( \dfrac{x}{a} \bigg)^{ \dfrac{2}{3} } + \bigg( \dfrac{y}{b} \bigg)^{ \dfrac{2}{3} } = 1$

⠀⠀⠀⠀⠀${\rm{\pink{\underline{\underline{★Solution★}}}}}$

$\: \: \: {Cos}^{3 } ∅ = \frac{x}{a} \\ \: \:$--------(1)

$\: \: \: {Sin}^{3 } ∅ = \frac{x}{b}$-------(2)

$\: \: \:\: \:\:\:\:\:putting\:Values$

$( {cos}^{3 }∅ ) { }^{ \frac{2}{3 } } + ( {sin}^{3} ∅){ }^{ \frac{2}{3 } } = 1$

$\: \: \: cancelling \: 3 \: in \: both \: terms$

$\:\:\: \:\:{cos}^{2 }∅ + {sin}^{2 } ∅ = 1$

$\: \: \: \: \:\:\:\:\: \: 1 \: = 1$

Hence proved!!

Answer 2

Heyaa ‼️

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